102 SIR B. C. BRODIE ON THE CALCULUS OE CHEMICAL OPERATIONS. 
This equation vanishes when x=%, and may be thus expressed 
a(a<Px 2 + +a<p| 2 — 3)(%- — £) = 0, 
whence the event is constituted as follows — 
«(a^ 2 — 1 )(*— |) ■ + «( a< Pz£ “ 1 Xz “ £) + a(«p£ 2 — • 1 )(z ~ I) = ' 0 5 
which equation may be resolved into the three equations 
«(a<PZ 2 — 1 )(Z-|) = °> 
a(a^ 2 -l)(^— 1) = 0, 
the results being 
“ 2 < PZ 3 + a ^= a 2 | ?Z 2 l+ a Z’ 
a 2 p* 2 £ + a t =ct2( PxZ 2 + a X’ 
a 2 Pz£ 2 + a £ =a 'W + a Z- 
No one of these phenomena has hitherto been realized; but we are thus led to 
anticipate their future realization. The unit a. 2 <px% 2 , which is characterized by the 
property of being, together with a unit of water, resoluble into a unit of phosphorous 
acid and a unit of hydrochloric acid, is (what may he termed) the unit of the mono- 
chlorhydrin of phosphorous acid, the unit a 2 <p^ 2 ^ being the dichlorhydrin of the same 
substance, the existence of which is also indicated to us by a variety of other consi- 
derations. 
(7) A unit of the trichlorhydrin of glycerin and three units of sulphide of hydrogen 
are resoluble into three units of hydrochloric acid and a unit of trithioglycerin — 
a 4 x 3 z 3 + 3a$=3a;£ -}- a 4 x 3 $ 3 . 
This equation may be thus expressed 
a(a 3 ;c 3 0 2 + a 3 x 3 ^0 -J-a 3 « 3 ^ 2 — 3)(^ — $) = 0, 
the event being constituted as follows — 
a(aV4 2 — 1 )(% — 0)+a(aV 3 ;^ — !)(%■ — &) + a(a V* 2 — 1)(% — 6 ) — 0 ; 
whence we have as the constituents of the event, 
«(aW-l)fc-fl)=0, 
a(ay^-l)( % ~3) = 0, 
a(aVy — l)(z — 6 ) = 0, 
or 
a 4 x 3 6%-fa3=a%-f a 4 x 3 ^ 3 , 
a 4 x 3 ^ 2 +afl=ax+a 4 xy, 
a 4 « 3 Z 3 + a0 = a;£ -f" a 4 « 3 ^ 2 ^- 
